Question

by what number please tell
​

Answer 1

Step-by-step explanation:

Correct answer is x=(3/2)^3

Answer 2

Question:

By what number should ( 4/9 )^-5 be multiplied as so to get ( 2/3 )^ -2 .

Solution :

Let us assume that the required number to be multiplied by is x.

> ( 4/9 )^-5 × x = ( 2/3 )^ -2

> [ 2/3 ]² ^ -5 × x = ( 2/3 )^-2

> ( 2/3 )^-10 × x = (2/3)^-2

x = [ (2/3)^-2 ]/[ (2/3)^-10 ]

> x = [ ( 2/3 ) ]^ -2 + 10

> x = (2/3)^8

This is the required answer.

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Additional Information :

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

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